Osadebe and on-loan defender Adedeji Oshilaja both struck in the first half before John Egan scored against his former side and Bradley Dack completed proceedings to get Gillingham’s campaign off to a flying start.
Gills boss Justin Edinburgh included five debutants from the start and two of them linked up for the opener, Ryan Jackson’s long throw causing mayhem in the box and Osadebe poking home.
The visitors struggled to get into the game – Che Adams their best outlet – and were 2-0 down two minutes before the break when Oshilaja stabbed the ball home after United had failed to clear a corner.
Egan made it three in the 82nd minute, meeting Brennan Dickenson’s corner to head home and the Gills added a fourth in injury time.
Dack capped a superb performance by driving a shot past despairing Blades goalkeeper George Long to round off a miserable afternoon for the visitors.